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- Deduction of the second derivative criterion for optimization of functions <br> of two variables using and as related to Taylorfor the function find the relative maxima, relative minima, and horizontal points of inflection. y=1/3x^3+x^2-24x+15 relative maxima (x,y)= relative minima (x,y)= horizontal points of inflection (x,y)=A right triangle has one vertex on the graph of y = x3, x > 0, at (x, y) another at the origin, and the third on the positive y-axis at (0, y). Express the area A of the triangle as a function of x.
- Application of derivative Optimization We are going to fence in a rectangular field that encloses 200 m2. If the cost of the material for of one pair of parallel sides is $3/m and cost of the material for the other pair of parallel sides is $8/m determine the dimensions of the field that will minimize the cost to build the fence around the field.Application of derivative Optimization We are going to fence in a rectangular field. Starting at the bottom of the field and moving around the field in a counter clockwise manner the cost of material for each side is $6/ft, $9/ft, $12/ft and $14/ft respectively. If we have $1000 to buy fencing material determine the dimensions of the field that will maximize the enclosed.Find all local maximum and minimum for f(x) = 2x3 + 3x2 -12x using the first derivative test. Show me your table.
- Find the absolute extrema of the function on the closed interval. Use a graphing utility to verify your results. f(x) = x3 − 12x, [0, 5]Find all the critical points and horizontal and vertical asymptotes of the function f(x)=(x^2+5)/(x-2). Use the First and/or Second Derivative Test to determine whether each critical point is a local maximum, a local minimum, or neither. You may use either test, or both, but you must show your use of the test(s). You do not need to identify any global extrema.A right triangle has one vertex on the graph of y=x3,x >0 at another at the origin,and the third on the positive y-axis at as shown in the figure.Express the area A of the triangle as a function of x.
- (Differentiation) 6.1.1) Fine slope of graph f(x) = 25-3x-x^2 when x = 2 and x = 1/2Find the absolute extrema of the function on the closed interval. find the minimum and maximum g(x) = 8x2/x-2 , [−2, 1]Polynomial Function of Data y = 1.2889x3 - 358.53x2 + 48536x - 34188 What is the second derivative, what is the point of inflection Explain the implications of the point of inflection